Plan ahead. You will need to start this approximately 8 hours before dinner time.

I prefer the slow cooked in a crock-pot method for preparing
a corned beef brisket over boiling it in a pot.
Boiling in a pot will take less time, but requires more attention.
I also think that the meat is more tender and flavorful when slow cooked.

Place the corned beef brisket in the crock-pot. Add a bottle of your
favorite beer, a handful of peppercorns, and a couple of bay leaves.
Add 2-3 cups water, enough to cover the brisket and begin heating on
high. Cut a small onion into large cubes and add them to the pot.

I usually wait 2 hours before adding the potatoes and carrots.
Wash the potatoes, remove any eyes, leave the skins on, and cut into
quarters. Peel carrots and cut into 3-4 inch long "logs".
Add these vegetables to the water, adding another cup or so of water if
necessary to cover everything with liquid. Continue cooking in
the crock-pot on high for another 2 hours.

About half way through the cooking process when everything seems to be
cooking away nicely in the crock-pot, I usually switch to low heat and
let it continue cooking for another 4 hours. Continue cooking until
the meat is VERY tender. Cooking times can vary depending on the crock-pot
and size/quantity of food inside. Expect 6-9 hours.

Shortly before serving chop the cabbage into
course chunks and add it to the crock-pot
during the last 15 minutes of cooking. Don't overcook.

To serve. Remove the brisket to a platter and slice into pieces.
The meat will probably be nearly falling apart at this point.
Use a slotted spoon to remove the vegetables and spread them
around the meat on the platter. If desired, spoon a little
of the leftover liquid over everything on the platter. Enjoy!